Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing

This Question is Closed

SithsAndGiggles Group TitleBest ResponseYou've already chosen the best response.2
Recall the distance formula: \[d^2=(xx_0)^2+(yy_0)^2\] In this particular problem, you have \((x_0,y_0)=(0,0)\) (the origin), since you want to find the distance between any given point on the curve \((x,y)\) and the origin. \[d^2=x^2+y^2\] Substitute the given equation of the curve: \[d^2=x^2+\left(4\sqrt{2x+2}\right)^2\\ d^2=x^2+16(2x+2)\\ d^2=x^2+32x+32\] Now differentiate both sides implicitly with respect to some dummy variable \(t\): \[2d\frac{dd}{dt}=(2x+32)\frac{dx}{dt}\] You're told that at the point \((1,8)\), \(x\) is increasing at a rate of 3 units/s, which translates to \(\dfrac{dx}{dt}=3\). \[2d\frac{dd}{dt}=(2\cdot1+32)(3)\\ 2d\frac{dd}{dt}=102\] You're asked to find \(\dfrac{dd}{dt}\), so first you need to find \(d\). To do this, find the distance between \((1,8)\) and \((0,0)\), then plug it into the above equation. Lastly, solve for \(\dfrac{dd}{dt}\).
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
@SithsAndGiggles omg thank you!! :)
 one year ago

SithsAndGiggles Group TitleBest ResponseYou've already chosen the best response.2
Yer welkum
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
@SithsAndGiggles hey, i found the distance which is 8 right? then i plugged in 8 into the equation and got 51/8... however, something is wrong?
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
i get \(\frac{19}{8}\)
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
oh nvm i got it.
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
it's 6.32577
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
to find the distance is this:
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
i got it... thank you! @satellite73
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
\[d^2=x^2+32x+32\] \[2dd'=2xx'+32x'\] \[dd'=xx'+32x'\] \[8d'=3+96\]
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
oh right doh
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
distance isn't 8 is it? distance is \(\sqrt{65}\)
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
which is pretty close to 8...
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
is the final answer \(\frac{99}{\sqrt{65}}\) ?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
close yes... i thought i had to do this: x2x1/y2y1
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
it's 51/sqrt(65)/65
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
oh damn i forgot to divide 32 by 2 must be past my bedtime
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.